Dense monolayers of living cells display intriguing relaxation dynamics, reminiscent of soft and glassy materials close to the jamming transition, and migrate collectively when space is available, as in wound healing or in cancer invasion. Here we show that collective cell migration occurs in bursts that are similar to those recorded in the propagation of cracks, fluid fronts in porous media, and ferromagnetic domain walls. In analogy with these systems, the distribution of activity bursts displays scaling laws that are universal in different cell types and for cells moving on different substrates. The main features of the invasion dynamics are quantitatively captured by a model of interacting active particles moving in a disordered landscape. Our results illustrate that collective motion of living cells is analogous to the corresponding dynamics in driven, but inanimate, systems.collective cell migration | avalanches | universality | vascular endothelial cadherin | collagen substrate C ollective cell movement depends on intracellular biological mechanisms as well as environmental cues due to the extracellular matrix (1-5), mainly composed of collagen which is organized in hierarchical structures, such as fibrils and fibers. The mechanical properties of collagen fibril networks are essential to offer little resistance and high sensitivity to small deformations, allowing easy local remodeling and strong strain stiffening needed to ensure cell and tissue integrity (6). Wound healing is a typical biological assay to study collective migration of cells under controlled conditions in vitro and is a prototypical experimental method to study active matter (7-10). Experiments performed on soluble collagen (11) or other gels (12), micropatterned (13, 14) and deformable substrates (1) show that cell migration is guided by the substrate structure and stiffness (5,15,16).It has been argued that collective migration properties arise from stresses transmitted between neighboring cells (1) giving rise to longranged stress waves in the monolayer (17,18). Hence the dynamics of an invading cell sheet is ruled by a combination of long-range internal stresses and interactions with the substrate, suggesting an analogy with driven elastic systems moving in a disordered medium such as cracks lines (19,20), imbibition fronts (21), or ferromagnetic domain walls (22). The scaling laws in these systems are usually associated with a depinning critical point that has been widely studied by simple models for interface dynamics. Thanks to a combination of numerical simulations (23, 24) and renormalization group theory (23,(25)(26)(27), we now have a detailed picture of the nonequilibrium phase transitions and universality classes in these systems. Here we substantiate the analogy between collective cell migration and depinning by revealing and characterizing widely distributed bursts of activity in the collective migration of different types of cells (human cancer cells and epithelial cells, mouse endothelial cells) over different substrates ...